LOGISTICRE-GRESS.co N DALPIAZ 10/2/2019 SO - tutto " - - PowerPoint PPT Presentation

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LOGISTICRE-GRESS.co N DALPIAZ 10/2/2019 SO - tutto " - - PowerPoint PPT Presentation

Nov 05, 2023 123 likes •234 views

LOGISTICRE-GRESS.co N DALPIAZ 10/2/2019 SO - tutto " Distr CLASSIFIER FAR ESTIMATED - - - > , y y TIX OF Die ( x ) ( ( x ) CREATE USING " near " x - K - Yi of Proportion ] [ Y K / X = = Pk ( x )

slide-1
SLIDE 1

LOGISTICRE-GRESS.co

N DALPIAZ 10/2/2019
slide-2
SLIDE 2 SO FAR
  • y
> CLASSIFIER

y

, ESTIMATED Distr
  • tutto "
OF TIX CREATE

( (x )

USING Die ( x ) Pk ( x ) =

[ Y

= K / X = ×] = Proportion
  • f
Yi
  • K
" near " x ↳ KNN ( NEIGHBORS )

↳

TREES ( NEIGHBORHOODS )
  • NON
  • PARAM
TMC MODELS Now .
  • .
A PARAMETRIC METHOD For BINARY CLASSIFICATION
slide-3
SLIDE 3

⑦ / NARY

CLASSIFICATION

T.fi

: DEFINEOUR

Focus →

p(x )

= P[ x
  • l
l X
  • If
I
  • p ( x )
  • P ( Y
  • o Ix
  • x)
slide-4
SLIDE 4

LOGISTIC

REGRESSION
  • log

)

=

Bot B. x ,

+ Bexz t
  • + Bpxp
  • ! .

#

UN2

COMBINATION OF FEATURES @ Bo + Bix , t
  • .
+ Bp =t
  • pCy=ilx=7

ffx.rs)

slide-5
SLIDE 5

LOGISTIC

REGRESSION function
  • f
X 'S AND B 'S
  • XIX
  • BERN ( p#

( CMPARE

To CTLDINARY LINEAR REGRESSION
  • Y )
X n N ( B. + B. x. t
  • -
→ Bpxp , r )
  • /
EXTRA PARAMETER
slide-6
SLIDE 6

DEFINE

  • legit (3)
= log (¥) r (3) = logit
  • ' (3)
= 1¥ = logit : co . .] → R M ( x) = Bo + B. x , t
  • Bp xp
r : IR → [ o . D
  • log (,P!×¥)
=

Bot B. x ,

t Bex z t
  • t Bp xp

logit ( elx))

= 7 ( x)

" " run

. ,e÷÷.=÷÷:÷÷÷÷
slide-7
SLIDE 7

Examine

log

)

= 4 + 2x ,
  • 2x .
Note pfx )
  • 0.5
⇒ 761=0 C) = 4 + 2x .
  • 2x .

(f)

" ° Xr ⇒ x , = 2 + x ,

f

n 7 (x. =
  • 2. xie)
/ ) : p Cx )
  • 0.5
" DECISION BOUNDARY "

pa.z.xi.os-i.ee#..o--o.aaa6

↳ ( x ,=z ,

xa
  • o)

I

/
  • c. ( x )
  • I

P(x.

=
  • 2. x. =L)
= Ite = 0.01799 ✓
slide-8
SLIDE 8

FTTINGLOGlsiictc.DE#

log (

)

= Bot B. x Xi Yi p (x;) SEQUENCE : l , t ' O
  • Z
t PROBABILITY : p (x .) op ( x . )
  • (
l
  • p (x .))
3 I ' i

f)

" 3 I CONDITIONAL.LI/SELlHoo# 5 I 4 °

L( B.

. B.) = .¥P[Yi
  • silk
.
  • 5
O
  • / }
' BE 7 MAXIMIZE / 6 O
slide-9
SLIDE 9

L ( B.

. B.) = !÷P[Yi
  • si Ix :-.
= . pix :) ' '
  • fi
  • axis)
" ' log L ( Bo , B .) = . y .
  • log ( p Gi))
t € , (l
  • yi) log (
I
  • p Cx:))

÷÷ --

CLASS O =

.IE

log ( l - plxi)) t !?y : log = E. log ft
  • E÷÷:)
.

sits .

  • axis
=
  • !§ log (
I + e " " ' " ) + y:( Botox:)
slide-10
SLIDE 10 log L ( Bo , B .) =
  • ,€ log ( Ite
" " " ) + y:( Botox:)

÷÷÷:÷:÷:÷÷÷÷÷÷:÷÷÷

.is:7

. * NO CLOSED FORM SOLUTION ' "

÷÷÷÷÷÷÷÷÷÷÷÷÷l

" :¥÷÷÷÷

.